Why I love working with my kids

Saw this problem yesterday via a Fawn Nguyen tweet:

Thought it would be a fun problem to talk through with the boys, but then my older son had to run an errand with wife so it ended up just being my younger son.

His approach just blew me away. I’m so glad to have the opportunity to have conversations like this with my kids:

[update from the day after originally publishing follows]

This morning I went through the question with my older son. He struggled with the problem much more than my younger son did. One of the contributing factors to his struggle is that he chose to keep track of the number of leaves on the ground rather than the number that fell each minute.

It was interesting to watch him work through the difficulties. He looked for lots of different patterns before finding the right one. I broke up his solution into 3 parts:

$1 + 2^1 + 2^2 + \ldots + 2^n$

He had a neat approach, which was essentially mathematical induction. You know that 1 + 2 is 4 – 1. That helps you see that 1 + 2 + 4 is 8 – 1, and so on. That was a neat way to think about the sum and led to a fun (and basic) conversation about mathematical induction.

Thanks to the Math Forum for this fun problem.